Parametric Evolution for a Deformed Cavity
Abstract
We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = <n(x)|m(x0)>, also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.
Cite
@article{arxiv.nlin/0008040,
title = {Parametric Evolution for a Deformed Cavity},
author = {Doron Cohen and Alex Barnett and Eric J. Heller},
journal= {arXiv preprint arXiv:nlin/0008040},
year = {2009}
}
Comments
13 pages, 8 figures, improved introduction, to be published in Phys. Rev. E